Speaker: Cheng ZHANG (Tsinghua University)

Time： April 28, 16:00-17:00

Place： 5505

Title： Sharp Lp estimates and size of nodal sets of generalized Steklov eigenfunctions

Abstract： We prove sharp Lp estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their L2 norms on the boundary. We prove it by establishing Lp bounds for the harmonic extension operators as well as the spectral projection operators on the boundary. Moreover, we derive lower bounds on the size of nodal sets for a variation of the Steklov spectral problem. We consider a generalized version of the Steklov problem by adding a non-smooth potential on the boundary but some of our results are new even without potential.